Mathematics

Thrust-to-weight ratio (TWR)

This is Newton's Second Law. If the ratio is less than 1 the craft will not lift off the ground. Note that the local gravitational acceleration, which is usually the surface gravity of the body the rocket is starting from, is required.

True Δv of a stage that crosses from atmosphere to vacuum

Calculation of a rocket stage's Δv, taking into account transitioning from atmosphere to vacuum. Δvout is the amount of Δv required to leave a body's atmosphere, not reach orbit. This equation is useful to figure out the actual Δv of a stage that transitions from atmosphere to vacuum.

Maximum Δv chart

This chart is a quick guide to what engine to use for a single stage interplanetary ship. No matter how much fuel you add you will never reach these ΔV without staging to shed mass or using the slingshot maneuver. (These calculations use a full/empty fuel-tank mass ratio of 9 for all engines except those noted.)

ISP(Vac) (s)

Max Δv (m/s)

Engines

Remarks

250

5249

O-10 "Puff"

Monopropellant (max full/empty mass ratio = 8.5)

290

6249

LV-1R "Spider" 24-77 "Twitch"

300

6464

KR-1x2 "Twin-Boar"

305

6572

CR-7 R.A.P.I.E.R. Mk-55 "Thud"

310

6680

LV-T30 "Reliant" RE-M3 "Mainsail"

315

6787

LV-1 "Ant" KS-25 "Vector" KS-25x4 "Mammoth"

320

6895

48-7S "Spark" LV-T45 "Swivel" RE-I5 "Skipper"

340

7326

KR-2L+ "Rhino" T-1 "Dart"

345

7434

LV-909 "Terrier"

350

7542

RE-L10 "Poodle"

800

17238

LV-N "Nerv"

4200

58783

IX-6315 "Dawn"

Xenon (max full/empty mass ratio = 4.167)

(Version: 1.6.1)

Math examples

TWR

Copy template:

TWR = F / (m * g) > 1

Isp

When Isp is the same for all engines in a stage, then the Isp is equal to a single engine. So six 200 Isp engines still yields only 200 Isp.

When Isp is different for engines in a single stage, then use the following equation:

This calculation only uses the mass of the fuel tanks and so the ln ( Mstart / Mdry ) part of the Δv equation has been replaced by a constant as Mstart / Mdry is always 9 (or worse with some fuel tanks) regardless of how many fuel tanks you use.

The following example will use a single stage and fuel tanks in the T-100 to Jumbo 64 range with an engine that outputs 380 seconds Isp.

Δv = 2.1972245773 × 380 seconds Isp × 9.82m/s² = Maximum Δv of 8199.1632327878 m/s (Replaced the log of mass with a constant as the ratio of total mass to dry mass is constant regardless of the number of tanks used as there is no other mass involved)

Δv = 21.576745349086 × 380 seconds Isp = Maximum Δv of 8199.1632327878 m/s (Reduced to its most simple form by combining all the constants)

True Δv

How to calculate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.

Assumption: It takes roughly 2500 m/s of Δv to escape Kerbin's atmosphere before vacuum Δv values take over for the stage powering the transition (actual value ranges between 2000 m/s and 3400 m/s depending on ascent). Note that, as of KSP 1.3.1, around 3800 m/s of Δv is required to reach an 80km orbit from the KSC.

Note: This equation is a guess, an approximation, and is not 100% accurate. Per forum user stupid_chris who came up with the equation: "The results will vary a bit depending on your TWR and such, but it should usually be pretty darn accurate."